On the 0-dimensional cusps of the Kahler moduli of a K3 surface

TL;DR

This paper establishes a correspondence between 0-dimensional cusps of the Kahler moduli space of a projective K3 surface and its twisted Fourier-Mukai partners, providing a counting formula and explicit cases.

Contribution

It introduces a novel bijective correspondence and counting formula linking cusps of the Kahler moduli to twisted Fourier-Mukai partners of K3 surfaces.

Findings

Bijection between cusps and twisted Fourier-Mukai partners

Counting formula for 0-dimensional cusps

Explicit calculation for Picard number 1 case

Abstract

Let S be a projective K3 surface. It is proved that the 0-dimensional cusps of the Kahler moduli of S are in one-to-one correspondence with the twisted Fourier-Mukai partners of S. This leads to a counting formula for the 0-dimensional cusps of the Kahler moduli. Applications to rational maps between K3 surfaces with large Picard numbers are given. When the Picard number of S is 1, the bijective correspondence is calculated explicitly.